Monod term

Microbial growth is the core of the biochemical reactions in the TBC model. This growth is linked to substrate and electron acceptor concentrations via Monod-terms. The back-coupling between microbial growth and reactive species consumption is performed via turnover coefficients and stoichiometric relationships. The basic equations are exemplified for a single microbial group X, one substrate S and one electron acceptor E ... 

As we have noted above, we can approximate the Monod term as because the substrate concentrations greatly exceed the value of K. Under these circumstances we can say that the total masses of substrate and biomass obey the relation... 

For the Nernst-Monod term expression, the f and Eka variables were originally defined in MATLAB and needed to be first sent to COMSOL using the fem.const command as shown previously. The variable E is a solution component (i.e., dependent variable) of a generic PDE application mode that is described in detail later. It is only defined in COMSOL, and thus, it was not necessary to declare it in MATLAB or send it via the fem.const command. Likewise, for the specific rate of substrate utilization expression, q 5, and were defined in MATLAB, whereas S and Mo are the solution components of the diffusion application mode. Note that in MATLAB and COMSOL, we do not use subscripts instead, we use regular fonts. Because the expression contains both COMSOL defined and MATLAB defined variables, the expression must be in single quotes. 

What Are the Theoretical Maximum Biofilm Thicknesses for Different Conductivities While biofilms may grow thick enough to restrict cells at their base from receiving nutrients, for practical applications, it is often desirable to have a biofilm that is entirely active across its thickness. To determine the maximum theoretical biofilm thickness, the model is restricted to cases where the biofilm is not substrate limited and the entire biofilm is active. We define the limiting biofilm thickness to be the distance at which the Nernst-Monod term drops to below 0.01 (the point in the biofilm where the biofilm activity is restricted to just 1 % of by potential drop lim-... 

Because of the crucial role of this enzyme in one of the most important bicxrhemical pathways in the cell, its allosteric properties have been studied extensively in solution. Interpretation of these studies in terms of the theory of allosteric enzymes led Monod and coworkers to conclude that ... 

The results obtained by measuring the affinity to oxygen in the presence of various monohydric alcohols (methanol, ethanol, 2-propanol, 1-propanol) 140-144> were interpreted in terms of the Monod-Wyman-Changeux model145), by which the change of the standard free-energy difference between R and T state in the absence of oxygen, due to the addition of alcohol, can be determined, i.e. 

In the present study, the UASB reactor was modeled in terms of the dispersed plug flow and the Monod type of rate equations to constmct the differential mass balance equations fcs- the anaerobic biodegradation of single and multiple substrates components of the volatile fetty acids. 

If the concentrations of only the electron donor and acceptor are considered to vary, each mD+ is invariant and the term ] [ n/ 1 in Equation 18.23 reverts to a half-saturation constant K[y Similarly, the corresponding term in Equation 18.24 may be represented by K A. Now, we see the dual Monod equation (Eqn. 18.16) is a specific simplification of the general rate law (Eqn. 18.22). 

Substrate-limited growth in terms of reduced availability of both the electron donor and the electron acceptor is common in wastewater of sewer systems. Based on the concept of Michaelis-Menten s kinetics for enzymatic processes, Monod (1949) formulated, in operational terms, the relationship between the actual and the maximal specific growth rate constants and the concentration of a limiting substrate [cf. Equation (2.14)] ... 

The relationship between i. and S as depicted in Figure 2.7 is relevant because it quantifies the importance of a substrate in terms of its concentration on the growth rate. As seen from Equation (2.16), X= 1/2 imax for S=Ks. For this reason, Ks is also named the half saturation constant. Equation (2.16) and the corresponding curves shown in Figure 2.7 are called the Monod expression and Monod curve, respectively. 

Oxygen is assumed to be present only in the liquid phase. The biomass is assumed to follow Monod growth kinetics, depending on both the oxygen and substrate concentrations in the liquid phase and to decline according to a first order decay term, where... 

In 1939, as part of his thesis, Jacques Monod proposed the equation which we use here. The thesis was published as a book in 1948 and was later condensed and translated into English in 1949 (see end-of-chapter reference). In microbiology they use the terms... 

Non-competitive inhibitors. These inhibitors bind to the enzyme or the enzyme-substrate complex at a site other than the active site. This results in a decrease in the maximum rate of reaction, but the substrate can still bind to the enzyme. An analogous concept is that of allosteric inhibition. The site of binding of an allosteric inhibitor is distinct from the substrate binding site. In this case, the inhibitor is not a steric analog of the substrate and instead binds to the allosteric site (the phenomenon was termed thus by Monod and Jacob). 

The most successful and widely used of the equations in Table 5.17 is that due to Monod and, although it may not be universally applicable, it gives a reasonable description of the variation of growth rate with substrate concentration in a surprisingly large number of cases. Whilst it does not allow for the lag phase at the beginning of a batch process, it may be modified by the addition of one extra term to allow for the consumption of cellular material to produce maintenance energy. 

When Cs is so low that the first term of the right-hand side of Eq. (6.17) is less than or equal to ke, the specific growth rate is equal to zero. These alternative models give a better fit for the growth of certain microorganisms, but their algebraic solutions are more difficult than for the Monod equation. 

There is a Cx term in the Monod equation which is not present in the Michaelis-Menten equation. 

As a result, this model can also predict the change of the average cell size with respect to time, which is not possible with the Monod model. Eqs. (6.73), (6.78), (6.79), and (6.80) can be expressed with the concentrations in terms of mass per unit culture volume as... 

A usual modification for this equation considers the influence of substrate concentration on the non-associated term, usually expressed as a Monod-type limitation (Equation 32). 

In the above dual-Monod equations, we note that competitive inhibition between the primary substrate and target contaminant is modeled by the C/KM and Cd/Kmd terms in the denominator on the right hand side of Eqs. (13)—(15), transformation product toxicity is modeled by the last term in Eq. (13), and deactivation is modeled by the FA parameter in Eq. (15). 

Another example is the Monod equation, which contains a concentration dependent term ... 

There are essentially two types of control mechanisms for biochemical switching allosteric cooperative transition and reversible chemical modification. Allosteric cooperativity, which was discussed in Chapter 4, was discovered in 1965 by Jacques Monod, Jefferies Wyman, and Jean-Picrrc Changeux [143], and independently by Daniel Koshland, George Nemethy and David Filmer [116]. The molecular basis of this phenomenon, which is well understood in terms of three-dimensional protein crystal structures and protein-ligand interaction, is covered in every biochemistry textbook [147] as well as special treatises [215],... 

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